You have $200,000 to invest for a year and have two choices. Bank A pays 8% annually, compounded annually. Bank B pays 8% annually, compounded quarterly. Which bank should you choose and why?

Bank B offers a higher final value. Therefore is more convenient.

Explanation:

Giving the following information:

You have $200,000 to invest for a year and have two choices. Bank A pays 8% annually, compounded annually. Bank B pays 8% annually, compounded quarterly.

The nominal interest rate is the same, but, the real interest rate should be higher for the option with quarterly compounded. This should be true because the interest gets to be part of the capital faster than an annual compounded. Higher the capital, the higher the interest.

We can prove that Bank B is better using the final value formula:

FV = PV * (1+i) ^n

Bank A:

FV = 200,000 * (1.08) = $216,000

Bank B:

i = 0.08/4 = 0.02

n=4

FV = 200,000 * (1.02^4) = $216,468.43

Bank B offers a higher final value. Therefore is more convenient.